Should I hash the password before sending it to the server side?

Since it's over HTTPS, it's definitely just fine to send the password without hashing (over HTTPS it's not plaintext). Furthermore, if your application is depending on HTTPS to keep it's content secure, then it's useless to hash the password before sending it over HTTPS (i.e. if an attacker can unencrypt the data on the wire, you're screwed anyways)

Sending a hash over the wire completely defeats the purpose of the hash, because an attacker can simply send the hash and forget about the password. In a nutshell, a system that athenticates using a hash in clear text is wide open and can be compromise with nothing more than network sniffing.

No, in fact this would be a vulnerability. If the attacker is able to obtain the hash from the database, then he could use it to authenticate without needing to crack it. Under no circumstance should a user or an attacker be able to obtain a hashes password.

The whole point of hashing passwords is to add an extra layer of security. If an attacker is able to obtain the hash and salt from the database using SQL Injection or an insecure backup then he has to find the plain text by brute forcing it. John The Ripper is commonly used to break salted password hashes.

Not using https is a violation of the OWASP Top 10: A9-Insufficient Transport Layer Protection

EDIT: If in your implementation you calculate a sha256(client_salt+plain_text_password) and then calculate another hash on the server side sha256(server_salt+client_hash) then this is not a serious vulnerability. However, it is still susceptible to eavesdropping and replaying the request. Thus this is still a clear violation of WASP A9. However, this is still utilizing a message digest as a security layer.

The closest thing i have seen to a client-side replacement for https is a diffie-hellman in key exchange in javascript. However, this does prevent active MITM attacks and thus is till technicality a violation of OWASP A9. The Authors of the code agree that this is not a complete replacement for HTTPS, however it is better than nothing and better than a client-side hashing system.

This is an old question, but I felt the need to provide my opinion on this important matter. There is so much misinformation here

The OP never mentioned sending the password in clear over HTTP - only HTTPS, yet many seem to be responding to the question of sending a password over HTTP for some reason. That said:

I believe passwords should never be retained (let alone transmitted) in plain text. That means not kept on disk, or even in memory.

People responding here seem to think HTTPS is a silver bullet, which it is not. It certainly helps greatly however, and should be used in any authenticated session.

There is really no need to know what an original password is. All that is required is a reliable way to generate (and reliably re-generate) an authentication "key" based on the original text chosen by the user. In an ideal world this text should immediately generate a "key" by salting then irreversibly hashing it using an intentionally slow hash-algorithm (like bcrypt, to prevent Brute-force). Said salt should be unique to the user credential being generated. This "key" will be what your systems use as a password. This way if your systems ever get compromised in the future, these credentials will only ever be useful against your own organisation, and nowhere else where the user has been lazy and used the same password.

So we have a key. Now we need to clean up any trace of the password on the clients device.

Next we need to get that key to your systems. You should never transmit a key or password "in the clear". Not even over HTTPS. HTTPS is not impenetrable. In fact, many organisations can become a trusted MITM - not from an attack perspective, but to perform inspections on the traffic to implement their own security policies. This weakens HTTPS, and it is not the only way it happens (such as redirects to HTTP MITM attacks for example). Never assume it is secure.

To get around this, we encrypt the key with a once off nonce.
This nonce is unique for every submission of a key to your systems - even for the same credential during the same session if you need to send it multiple times. You can reverse said nonce (decrypt), once it arrives in your own systems to recover the authentication key, and authenticate the request.

At this point I would irreversibly hash it one last time before it is permanently stored in your own systems. That way you can share the credential's salt with partner organisations for the purposes of SSO and the like, whilst being able to prove your own organisation cannot impersonate the user. The best part of this approach is you are never sharing anything generated by the user without their authorisation.

Do more research, as there is more to it than even I have divulged, but if you want to provide true security to your users, I think this method is currently the most complete response here.

TL;DR:

Use HTTPS. Securely hash passwords, irreversibly, with a unique salt per password. Do this on the client - do not transmit their actual password. Transmitting the users original password to your servers is never "OK" or "Fine". Clean up any trace of the original password. Use a nonce regardless of HTTP/HTTPS. It is much more secure on many levels. (Answer to OP).